A deck of 52 playing cards is placed over-hanging the straight edge of a table. The cards are identical and uniformly dense. Suppose these cards are 3.5 inches in length, and this side is perpendicular to the table's edge. If the individual cards can be pushed forward or pulled back from the edge as you please, what is the farthest the cards can reach beyond the edge without any card tipping or leaning off of the card or table immediately below it?

Example of what a three-card deck may look like:
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[[[[Table]]]]]]]

(In reply to Ballast (pointer) by Jer)

Jer,
The only law governing this problem is that the center of gravity has to remain above the table.  Setting up a ballast on the first card will not change that.
If you want to set up a ballast on the second card, you will also have to set up a ballast for that second ballast.
If you do not position the ballast carefully, part of it will only put force on the table, and not on the card, and this implies that the cards will not be able to stick ot further.

So: I don't think a ballast can be of any help.

Edited on February 4, 2005, 8:35 pm

Posted by Hugo on 2005-02-04 20:34:24